Answer:
5.73 mg of the sample will be left in 25 days.
Explanation:
Given that:
Half life = 8 days
[tex]t_{1/2}=\frac {ln\ 2}{k}[/tex]
Where, k is rate constant
So,
[tex]k=\frac {ln\ 2}{t_{1/2}}[/tex]
[tex]k=\frac{ln\ 2}{8}\ days^{-1}[/tex]
The rate constant, k = 0.08664 days⁻¹
Time = 25 days
Using integrated rate law for first order kinetics as:
[tex][A_t]=[A_0]e^{-kt}[/tex]
Where,
[tex][A_t][/tex] is the concentration at time t
[tex][A_0][/tex] is the initial concentration = 50 mg
So,
[tex][A_t]=50\times e^{-0.08664\times 25}\ mg[/tex]
[tex][A_t]=5.73\ mg[/tex]
5.73 mg of the sample will be left in 25 days.
